{"id":{"repo_id":"gatech","oai_identifier":"oai:repository.gatech.edu:1853/49026"},"canonical_url":"https://search.dev.ndltd.org/etd/gatech/oai:repository.gatech.edu:1853/49026","repository":{"repo_id":"gatech","name":"Georgia Tech","base_url":"https://repository.gatech.edu/server/oai/request"},"display":{"title":"Geometric discretization schemes and differential complexes for elasticity","abstract":"In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton's principle on this configuration manifold. 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Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton's principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Geometric discretization schemes and differential complexes for elasticity"]}]}],"canonical_facts":{"dc:contributor.advisor":["Yavari, Arash"],"dc:contributor.committeemember":["Desroches, Reginald","Gangbo, Wilfrid","Garmestani, Hamid","Thadhani, Naresh"],"dc:contributor.department":["Civil and Environmental Engineering"],"dc:creator":["Angoshtari, Arzhang"],"dc:date.accessioned":["2013-09-20T13:24:41Z"],"dc:date.available":["2013-09-20T13:24:41Z"],"dc:date.issued":["2013-05-15"],"dc:description.abstract":["In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. 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